Question 1197832
let x equal the number of micro processors.
option A:
cost per micro processor = 10 dollars each.
y = 10x would be the cost, with y being the total cost and x being the number of micro processors.
option B:
y = 80,000 + 8x.
option C:
120,000 + 5x.


look for when option A is the smallest.


option A less than option B when 10x < 80,000 + 8x.
subtract 8x from both sides of this equation to get 2x < 80,000.
solve for x to get x = 40,000


option A less than option C when 10x <= 120,000 + 5x.
subtract 5x from both sides of this equation to get 5x < 120,000.
solve for x to get x = 24,000.


what this says is that option A is less than option B or C when x < 24000.


option B less than option C when 80,000 + 8x < 120,000 + 5x.
subtract 5x from both sides of the equation and subtract 80,000 from both sides of the equation to get 3x = 40,000.
solve for x to get x = 13,333.333.....
when x = 13,333, option B is less than option C.
when x = 13,334, option C is less than option B.


this suggests that option A is the cheapest from x = 0 to x < 24000 and option C is the cheapest from x > 24000.


note that option C is cheaper than option B when x = < 13,333.00, option A is cheaper than both of them at that point.


these equations can be graphed as shown below:


<img src = "http://theo.x10hosting.com/2022/110201.jpg">


let me know if you have any questions.
theo